Answer:
0.1172
Explanation:
The probability that a buyer prefers blue = 50% = 0.5
The number of buyers =10
We want to find the probability that exactly 3 buyers would prefer blue.
To solve this problem, we use the binomial distribution formula given below:
[tex]\begin{gathered} P(x=k)=\left(\begin{array}{l}n \\ k\end{array}\right)p^k(1-p)^{n-k} \\ =\frac{n!}{k!(n-k)!}p^k(1-p)^{n-k} \end{gathered}[/tex]
In the given case:
• n=10
,
• k=3
,
• p=0.5
Therefore:
[tex]\begin{gathered} P(x=3)=\frac{10!}{(10-3)!3!}(0.5)^3(1-0.5)^{10-3} \\ =\frac{10!}{7!3!}\times(0.5)^3(0.5)^7 \\ =\frac{10\times9\times8\times7!}{7!\times6}\times(0.5)^3\times(0.5)^7 \\ =\frac{10\times9\times8}{6}\times(0.5)^3\times(0.5)^7 \\ \approx0.1172 \end{gathered}[/tex]
The probability that exactly 3 buyers would prefer blue is 0.1172 (rounded to four decimal places).
